A multiple input multiple output (“MIMO” for short) radio system is capable of obtaining diversity and an array gain by means of transmit beamforming (“BF” for short)/precoding and receive signal combination. A signal vector received by a typical system that uses BF or precoding may be represented by the following equation (1):y=HVs+n  (1)where y represents the received signal vector, H represents a channel matrix, V represents a precoding matrix, s represents a transmitted symbol vector, and n represents measured noise.
Optimal precoding generally requires that a transmitter completely known channel state information (“CSI” for short). A common method is that a user equipment (“UE” for short) quantizes instantaneous CSI and feeds back the CSI to an evolved NodeB (“eNB” for short). In the release 8 (R8) of an existing Long Term Evolution (“LTE” for short) system, CSI information fed back by the UE may include information such as a rank indicator (“RI” for short), a precoding matrix indicator (“PMI” for short), and a channel quality indicator (“CQI” for short), where the RI and the PMI respectively indicate the number of layers and a precoding matrix that are used. A codebook of the LTE R8 is designed mainly for single user MIMO (“SU-MIMO” for short), where a precoding matrix or a code word needs to satisfy an 8 phase shift keying (“8PSK” for short) restraint, which limits precision of space quantization. This causes a serious limitation to performance of a transmission manner that is sensitive to space quantization precision, such as multi-user MIMO (“MU-MIMO” for short).
In order to satisfy a higher system requirement, a 3rd Generation Partnership Project (“3GPP” for short) LTE system needs to further enhance performance of MU-MIMO; moreover, a coordinated multi-point (“CoMP” for short) transmission technology is further introduced into the system. At present, the CoMP technology is based on single-cell feedback; therefore, both the foregoing two technologies raise higher requirements on feedback performance. Because a capacity of a feedback channel is limited, a size of a codebook set is also limited, which raises higher requirements on codebook designing.
A 3GPP LTE R8 system uses a single codebook, where a precoding matrix is indicated by an RI and a PMI. With respect to a 4-antenna system, correspondences between RIs, PMIs, and code words in a codebook are shown in the following Table 1:
TABLE 1RIPMIun12340u0 = [1 −1 −1 −1]TW0{1}W0{14}/{square root over (2)}W0{124}/{square root over (3)}W0{1234}/21u1 = [1 −j 1 j]TW1{1}W1{12}/{square root over (2)}W1{123}/{square root over (3)}W1{1234}/22u2 = [1 1 −1 1]TW2{1}W2{12}/{square root over (2)}W2{123}/{square root over (3)}W2{3214}/23u3 = [1 j 1 −j]TW3{1}W3{12}/{square root over (2)}W3{123}/{square root over (3)}W3{3214}/24u4 = [1 (−1 − j)/{square root over (2)} −j (1 − j)/{square root over (2)}]TW4{1}W4{14}/{square root over (2)}W4{124}/{square root over (3)}W4{1234}/25u5 = [1 (1 − j)/{square root over (2)} j (−1 − j)/{square root over (2)}]TW5{1}W5{14}/{square root over (2)}W5{124}/{square root over (3)}W5{1234}/26u6 = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{square root over (2)}]TW6{1}W6{13}/{square root over (2)}W6{134}/{square root over (3)}W6{1324}/27u7 = [1 (−1 + j)/{square root over (2)} j (1 + j)/{square root over (2)}]TW7{1}W7{13}/{square root over (2)}W7{134}/{square root over (3)}W7{1324}/28u8 = [1 −1 1 1]TW8{1}W8{12}/{square root over (2)}W8{124}/{square root over (3)}W8{1234}/29u9 = [1 −j −1 −j]TW9{1}W9{14}/{square root over (2)}W9{134}/{square root over (3)}W9{1234}/210u10 = [1 1 1 −1]TW10{1}W10{13}/{square root over (2)}W10{123}/{square root over (3)}W10{1324}/211u11 = [1 j −1 j]TW11{1}W11{13}/{square root over (2)}W11{134}/{square root over (3)}W11{1324}/212u12 = [1 −1 −1 1]TW12{1}W12{12}/{square root over (2)}W12{123}/{square root over (3)}W12{1234}/213u13 = [1 −1 1 −1]TW13{1}W13{13}/{square root over (2)}W13{123}/{square root over (3)}W13{1324}/214u14 = [1 1 −1 −1]TW14{1}W14{13}/{square root over (2)}W14{123}/{square root over (3)}W14{3214}/215u15 = [1 1 1 1]TW15{1}W15{12}/{square root over (2)}W15{123}/{square root over (3)}W15{1234}/2where Wn{s} represents a matrix formed by a column set {s} of a matrix Wn=I−2ununH/unHun, I is a 4×4 identity matrix, and un is given in the foregoing Table 1.
In the codebook of the R8 system, with respect to a precoding matrix whose rank is 1, precoding matrices whose indexes are 0 to 7 are discrete Fourier transform (“DFT” for short) vectors, where the DFT vectors are applicable to a uniform linear array (“ULA” for short) antenna. A DFT vector indicates a Tx1 precoding matrix, and the DFT vector v generally has a form shown in equation (2):v=[1ej2πm/N. . . ej2π(T−2)m/Nej2π(T−1)m/N]  (2),where N and m are integers, N=2x, where x is a nonnegative integer, that is, N is 2 raised to the power of x, and a tth element of the DFT vector v is ej2π(t−1)m/N (t=1, 2, . . . , T).
In a release 10 (R10) of the 3GPP LTE system, a codebook used by an 8-antenna system is formed by two groups of DFT vectors vm, and the two groups of DFT vectors have a phase difference φn, where the DFT vectors vm and the phase difference are represented by the following equation (3):vm=[1ej2πm/32ej4πm/32ej6πm/32]  (3)
The following provides a codebook structure of the 8-antenna system. The codebook structure is designed for a dual-polarized antenna. Table 2 shows an 8-antenna codebook when a rank is 1 (that is, the number of transmission layers is one layer), Table 3 shows the 8-antenna codebook when the rank is 2 (that is, the number of transmission layers is two layers), Table 4 shows the 8-antenna codebook when the rank is 3 (that is, the number of transmission layers is three layers), and Table 5 shows the 8-antenna codebook when the rank is 4 (that is, the number of transmission layers is four layers).
TABLE 2i2i1012345670-15W2i1,0(1)W2i1,1(1)W2i1,2(1)W2i1,3(1)W2i1+1,0(1)W2i1+1,1(1)W2i1+1,2(1)W2i1+1,3(1)i2i1891011121314150-15W2i1+2,0(1)W2i1+2,1(1)W2i1+2,2(1)W2i1+2,3(1)W2i1+3,0(1)W2i1+3,1(1)W2i1+3,2(1)W2i1+3,3(1)
      W          m      ,      n              (      1      )        =            1              8              ⁡          [                                                  v              m                                                                                          φ                n                            ⁢                              v                m                                                        ]      
TABLE 3i2i101230-15W2i1, 2i1, 0(2)W2i1, 2i1, 1(2)W2i1+1,2i1+1,0(2)W2i1+1,2i1+1,1(2)i2i145670-15W2i1+2,2i1+2,0(2)W2i1+2,2i1+2,1(2)W2i1+3,2i1+3,0(2)W2i1+3,2i1+3,1(2)i2i18910110-15W2i1,2i1+1,0(2)W2i1,2i1+1,1(2)W2i1+1,2i1+2,0(2)W2i1+1,2i1+2,1(2)i2i1121314150-15W2i1,2i1+3,0(2)W2i1,2i1+3,1(2)W2i1+1,2i1+3,0(2)W2i1+1,2i1+3,1(2)
      W          m      ,              m        ′            ,      n              (      2      )        =            1      4        ⁡          [                                                  v              m                                                          v                              m                ′                                                                                                        φ                n                            ⁢                              v                m                                                                                        -                                  φ                  n                                            ⁢                              v                                  m                  ′                                                                        ]      
TABLE 4i2i101230-3W8i1,8i1,8i1+8(3)W8i1+8,8i1,8i1+8(3){tilde over (W)}8i1,8i1+8,8i1+8(3){tilde over (W)}8i1+8,8i1,8i1(3)i2i145670-3W8i1+2,8i1+2,8i1+10(3)W8i1+10,8i1+2,8i1+10(3){tilde over (W)}8i1+2,8i1+10,8i1+10(3){tilde over (W)}8i1+10,8i1+2,8i1+2(3)i2i18910110-3W8i1+4,8i1+4,8i1+12(3)W8i1+12,8i1+4,8i1+12(3){tilde over (W)}8i1+4,8i1+12,8i1+12(3){tilde over (W)}8i1+12,8i1+4,8i1+4(3)i2i1121314150-3W8i1+6,8i1+6,8i1+14(3)W8i1+14,8i1+6,8i1+14(3){tilde over (W)}8i1+6,8i1+14,8i1+14(3){tilde over (W)}8i1+14,8i1+6,8i1+6(3)
  where  ,          ⁢            W              m        ,                  m          ′                ,                  m          ″                            (        3        )              =                  1                  24                    ⁡              [                                                            v                m                                                                    v                                  m                  ′                                                                                    v                                  m                  ″                                                                                                        v                m                                                                    -                                  v                                      m                    ′                                                                                                      -                                  v                                      m                    ″                                                                                      ]              ,          ⁢                    W        ~                    m        ,                  m          ′                ,                  m          ″                            (        3        )              =                  1                  24                    ⁡              [                                                            v                m                                                                    v                                  m                  ′                                                                                    v                                  m                  ″                                                                                                        v                m                                                                    v                                  m                  ′                                                                                    -                                  v                                      m                    ″                                                                                      ]            
TABLE 5i2i101230-3W8i1,8i1+8,0(4)W8i1,8i1+8,1(4)W8i1+2,8i1+10,0(4)W8i1+2,8i1+10,1(4)i2i145670-3W8i1+4,8i1+12,0(4)W8i1+4,8i1+12,1(4)W8i1+6,8i1+14,0(4)W8i1+6,8i1+14,1(4)
      W          m      ,              m        ′            ,      n              (      4      )        =            1              32              ⁡          [                                                  v              m                                                          v                              m                ′                                                                        v              m                                                          v                              m                ′                                                                                                        φ                n                            ⁢                              v                m                                                                                        φ                n                            ⁢                              v                                  m                  ′                                                                                                        -                                  φ                  n                                            ⁢                              v                m                                                                                        -                                  φ                  n                                            ⁢                              v                                  m                  ′                                                                        ]      
An index of an 8-antenna precoding matrix may be represented by a first codebook index i1 and a second codebook index i2; with respect to the 8-antenna codebook whose rank is 1, both the first codebook index i1 and the second codebook index i2 need to be represented by four bits. In order to save an overhead of a feedback resource, a PMI may be represented by four bits. This requires that subsampling be performed on the PMI or the 8-antenna codebook, where a sampling codebook in a submode 2 of a physical uplink control channel (“PUCCH” for short) mode 1-1 of the 8-antenna system is shown in Table 6:
TABLE 6FirstTotalPMIFirst CodebookSecond PMISecond CodebookNumberRIIPMI1Index i1IPMI2Index i2of Bits10-72IPMI10-12IPMI2420-72IPMI10-1IPMI2430-12IPMI10-74└IPMI2/4┘ + IPMI2440-12IPMI10-7IPMI2450-3IPMI100260-3IPMI100270-3IPMI1002800000
With respect to an enhanced 4-antenna codebook, in order to improve system performance without increasing complexity of codebook designing and feedback, the codebook structure design solution of the 8-antenna system may be used, and an index of a precoding matrix may also be represented by a first codebook index i1 and a second codebook index i2. In order to save an overhead of a feedback resource, a PMI may also be represented by four bits; this also requires that subsampling be performed on the PMI or the 4-antenna codebook.
However, with respect to a latest 4-antenna codebook used by the 3GPP LTE system, when a mode is the submode 2 of the PUCCH mode 1-1, after subsampling is performed on a codebook according to the 8-antenna subsampling table shown in Table 6, when a rank is 1, a precoding matrix has only two DFT vectors. However, a 4-antenna codebook of an R8 system has eight DFT vectors. Therefore, when a configured antenna is a uniform linear array ULA antenna, for the enhanced 4-antenna codebook in the submode 2 of the PUCCH mode 1-1, precoding matrices that are applicable to the ULA antenna are less than precoding matrices of the R8 system, and therefore performance deterioration is severe.